Logarithmic Corrections in the 2D XY Model

Using two sets of high-precision Monte Carlo data for the twodimensional XY model in the Villain formulation on square L×L lattices, the scaling behavior of the susceptibility χ and correlation length ξ at the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections (lnL)−2r in the finite-size scaling region and (ln ξ)−2r in the high-temperature phase near criticality, respectively. By analyzing the susceptibility at criticality on lattices of size up to 512 we obtain r = −0.0270(10), in agreement with recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang zeros in the cosine formulation of the XY model. By studying susceptibilities and correlation lengths up to ξ ≈ 140 in the hightemperature phase, however, we arrive at quite a different estimate of r = 0.0560(17), which is in good agreement with recent analyses of thermodynamic Monte Carlo data and high-temperature series expansions of the cosine formulation. PACS numbers: 05.50.+q, 75.10.Hk, 64.60.Cn, 11.15.Ha